The Localized Orthogonal Decomposition (LOD) [1]}, which itself is based on the Variational Multiscale Method (VMM) [2]}, instead makes use of a splitting of the full fine-scale approximation space into a negligible fine-scale component and an orthogonal multiscale space in which the solution is sought.
This multiscale space is then approximated by computing localized approximations of the orthogonal projection into the finescale space (corrector problems).
For an extensive overview of the LOD, we refer to [3]} and the references therein.
In this work we consider a Petrov–Galerkin formulation of the LOD [4]},
which has lower storage and communication requirements for the computed fine-scale data in comparison to the original Galerkin formulation.
